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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2021 · Mathematics · Quadratic Equation

If θ and θ are the roots of the equation a x^2+b x+c=0 , then which...

If sin⁡θ\sin \theta and cos⁡θ\cos \theta are the roots of the equation ax2+bx+c=0a x^2+b x+c=0, then which one of the following is correct?

Options

  1. Aa2+b2−2ac=0a^2+b^2-2 a c=0
  2. B−a2+b2+2ac=0-a^2+b^2+2 a c=0
  3. Ca2−b2+2ac=0a^2-b^2+2 a c=0
  4. Da2+b2+2ac=0a^2+b^2+2 a c=0

Correct answer

C. a2−b2+2ac=0a^2-b^2+2 a c=0

Step-by-step solution

Since, sin⁡θ\sin \theta and cos⁡θ\cos \theta are the roots of ax2+bx+c=0∴sin⁡θ+cos⁡θ=−baa x^2+b x+c=0\therefore \sin \theta+\cos \theta=\frac{-b}{a} and sin⁡θ⋅cos⁡θ=ca\sin \theta \cdot \cos \theta=\frac{c}{a} we have,(sin⁡θ+cos⁡θ)2=sin⁡2θ+cos⁡2θ+2sin⁡θ(\sin \theta+\cos \theta)^2=\sin ^2 \theta+\cos ^2 \theta+2 \sin \theta. cos⁡θ\cos \theta. ⇒a2−b2+2ac=0\Rightarrow a^2-b^2+2 a c=0
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